Spiderman's Workout

Staying fit is important for every super hero, and Spiderman
is no exception. Every day he undertakes a climbing exercise in
which he climbs a certain distance, rests for a minute, then
climbs again, rests again, and so on. The exercise is described
by a sequence of distances $d_1,
d_2,\ldots , d_ m$ telling how many meters he is to
climb before the first first break, before the second break,
and so on. From an exercise perspective it does not really
matter if he climbs up or down at the $i$:th climbing stage, but it is
practical to sometimes climb up and sometimes climb down so
that he both starts and finishes at street level. Obviously, he
can never be below street level. Also, he would like to use as
low a building as possible (he does not like to admit it, but
he is actually afraid of heights). The building must be at
least 2 meters higher than the highest point his feet
reach during the workout.

He wants your help in determining when he should go up and
when he should go down. The answer must be legal: it must start
and end at street level (0 meters above ground) and it may
never go below street level. Among the legal solutions he wants
one that minimizes the required building height. When looking
for a solution, you may not reorder the distances.

If the distances are 20 20 20 20 he can either climb
up, up, down, down or
up, down, up, down. Both are
legal, but the second one is better (in fact optimal) because
it only requires a building of height 22, whereas the first one
requires a building of height 42. If the distances are 3 2 5 3
1 2, an optimal legal solution is to go up, up, down, up, down, down. Note that for
some distance sequences there is no legal solution at all
(e.g., for 3 4 2 1 6 4 5).

Input

The first line of the input contains an integer $N$ giving the number of test
scenarios, $1 \le N \le
101$. The following $2N$ lines specify the test scenarios,
two lines per scenario: the first line gives a positive integer
$M \leq 40$ which is the
number of distances, and the following line contains the
$M$ positive integer
distances. For any scenario, the total distance climbed (the
sum of the distances in that scenario) is at most 1000.

Output

For each input scenario a single line should be output. This
line should either be the string “IMPOSSIBLE” if no legal
solution exists, or it should be a string of length
$M$ containing only the
characters “U” and “D”, where the $i$:th character indicates if
Spiderman should climb up or down at the $i$:th stage. If there are several
different legal and optimal solutions, output one of them (it
does not matter which one as long as it is optimal).